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PTAS for k-tour cover problem on the plane for moderately large values of k
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Adamaszek, Anna, Czumaj, Artur and Lingas, Andrzej (2010) PTAS for k-tour cover problem on the plane for moderately large values of k. International Journal of Foundations of Computer Science, Volume 21 (Number 6). pp. 893-904. doi:10.1142/S0129054110007623 ISSN 0129-0541.
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Official URL: http://dx.doi.org/10.1142/S0129054110007623
Abstract
Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P.
The k-tour cover problem is known to be NP-hard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomial-time approximation scheme (PTAS) for small values of k, k = circle divide (log n/ log log n).
In this paper, we significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of k <= 2(log delta n), where delta = delta(epsilon). The main technical result proved in the paper is a novel reduction of the k-tour cover problem with a set of n points to a small set of instances of the problem, each with circle divide((k/epsilon)(circle divide(1))) points.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Transportation problems (Programming), Approximation algorithms | ||||
| Journal or Publication Title: | International Journal of Foundations of Computer Science | ||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
| ISSN: | 0129-0541 | ||||
| Official Date: | December 2010 | ||||
| Dates: |
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| Volume: | Volume 21 | ||||
| Number: | Number 6 | ||||
| Page Range: | pp. 893-904 | ||||
| DOI: | 10.1142/S0129054110007623 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Sweden. Vetenskapsrådet [Research Council], University of Warwick. Centre for Discrete Mathematics and Its Applications | ||||
| Grant number: | EP/D063191/1 (EPSRC), 621-2005-408 (VR) | ||||
| Version or Related Resource: | Adamaszek, Anna, et al. (2009). PTAS for k-tour cover problem on the plane for moderately large values of k. Lecture Notes in Computer Science, 5878, pp. 994-1003. http://wrap.warwick.ac.uk/id/eprint/5481 | ||||
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